## Table 1. Definitions of benchmark cases

 Case Ra_0.5 Viscosity variation l and m for initial perturbation Resolution BM1A 7e3 1e0 (3,2) 32x(12×32×32) BM1B 7e3 1e1 (3,2) 32x(12×32×32) BM1C 7e3 2e1 (3,2) 32x(12×32×32) BM1D 7e3 1e2 (3,2) 32x(12×32×32) BM1E 7e3 1e3 (3,2) 32x(12×32×32) BM1F 7e3 1e4 (3,2) 32x(12×32×32) BM1G 7e3 1e5 (3,2) 32x(12×32×32) BM1H 7e3 1e6 (3,2) 32x(12×32×32) BM2A 7e3 1e0 (4,0)+(4,4) 32x(12×32×32) BM2B 7e3 2e1 (4,0)+(4,4) 32x(12×32×32) BM2C 7e3 3e1 (4,0)+(4,4) 32x(12×32×32) BM2D 7e3 1e2 (4,0)+(4,4) 32x(12×32×32) BM2E 7e3 1e3 4,0)+(4,4) 32x(12×32×32) BM2F 7e3 1e4 (4,0)+(4,4) 32x(12×32×32) BM2G 7e3 1e5 (4,0)+(4,4) 32x(12×32×32) BM2H 7e3 1e6 (4,0)+(4,4) 32x(12×32×32) BM3A 1e5 1e0 (4,0)+(4,4) 48x(12×48×48) BM3B 1e5 1e1 from BM3A 48x(12×48×48) BM3C 1e5 3e1 from BM3A 48x(12×48×48) BM3D 1e5 1e2 from BM3C 48x(12×48×48)

Note:

1) Resolution in radial direction (the number outside of the parentheses) for our calculations is refined near the top and bottom boundaries.

2) Resolution for comparison cases is 48x(6×48×48) for Stemmer et al. {2006}, 102x(102×204) for Yoshida and Kageyama {2004}, where the number outside parentheses represents the resolution in radial direction.

3) Ratcliff et al {1996} used different resolution for cubic and tetrahedral symmetry cases, as they considered the symmetry of these cases and did not compute them in a full sphere. For cubic symmetry cases, the equivalent resolution is 32, 64, and 128 cells in radial, co-latitude and longitude directions, respectively, and these numbers are 32, 32, and 64 for the tetrahedral cases.